RoFiRM Berichtzusammenfassung

During the first half of the ERC project, I have made a significant progress in the projects proposed in the application, thanks to the excellent team of collaborators recruited within the project.

Remarkable results have been obtained for the robust hedging problem, the martingale optimal transport on the line, and the corresponding connection with the Skorohod embedding problem. This problem is motivated by concrete questions related to model risk in financial engineering. I have also been successful in solving a very popular stochastic differential non-zero sum game which is at the basis of contract theory and moral hazard in economics. The major developments in contract theory are also modeled by appropriate extensions of this model which illustrate the relevant incentive mechanism. Our contribution is to provide a systematic method of resolution for this class of problems.

Finally, we have introduced a new class of Monte Carlo approximation for nonlinear parabolic PDEs based on an original representation in terms of marked branching diffusions. This is the very first genuinely high-dimensional numerical method for nonlinear PDEs.

All of our results are based on recent developments on the control of path-dependent stochastic systems. An important progress in this research area has been achieved within our team.